This is the first half of a two year, assignment driven course.
Timeframe
Content
Essential Questions
Skills
Resources
Assessment
Assignments 32-44
Polar coordinates & Complex Numbers
- definition of polar coordinates
- converting between polar and rectangular coordinates
- graphs of basic polar equations (circles, roses, spirals)
- rewriting equations between polar and rectangular form
- adding, subtracting, multiplying polar and rectangular points
- polar and rectangular definition of "i"
- complex form of polar / rectangular points
- operations on complex numbers
The student will:
- understand and apply the definition of polar coordinates
- convert between polar and rectangular coordinates
- graph the basic polar equations (circles, roses, spirals)
- rewrite equations between polar and rectangular form
- add, subtract, multiply polar and rectangular points
- understand and apply polar and rectangular definition of "i"
- understand and apply the complex form of polar / rectangular points
- perform operations on complex numbers
Questions on tests and quizzes
Assignments 49-61, 123-127
Sequences & Series
- definition of arithmetic sequence
- definition of geometric sequence
- recursive and explicit formulas for the Nth term of an arithmetic or geometric sequence
- explicit formulas for the Nth sum of an arithmetic or geometric sequence
- formula for the sum of an infinite geometric sequence
- derivation of amortized interest formula
- derivation of euler's formula ( e^i*pi+1=0)
The student will:
- understand and apply the definition of arithmetic sequence
- understand and apply the definition of geometric sequence
- write and apply both recursive and explicit formulas for the Nth term of an arithmetic or geometric sequence
- write and apply explicit formulas for the Nth sum of an arithmetic or geometric sequence
- write and apply formula for the sum of an infinite geometric sequence
- understand the derivation of amortized interest formula, and apply the formula to loan situations
- understand the derivation of euler's formula
( e^i*pi+1=0)
Assignments 1-7, 10, 13, 31, 32, 33
Subsets and operations of real numbers
- definition of rational and irrational
- irrationality of square roots
- which operations "distribute" correctly over others?
- nth roots, radicals and rational exponents
- density of integers, rationals, irrationals, etc.
- "rationalizing denominators"
- abstract definitions of identity element and inverse for a set under a given operation.
- definition of/ properties of base-N numeral
- conversion among base-N numbers.
How did irrationals allow early mathematicians to "fill in" the real number line?
The student will be able to define and give examples of rational and irrational numbers.
The student will be able to convert any decimal number into its equivalent rational form.
The student will be able to identify or complete correct examples of distribution.
The student will be able to understand the mathematical/technological representations of a "number".
The student will be able to rewrite radical expressions with rational denominators.
The student will be able to identify the identity element of a set, and identify the inverse of each element.
The student will be able to convert among base-N numbers.
Questions on written tests.
Assignments 1-7, 15, 18, 19, 23
Triangle trig
- area of a triangle (1/2 bh formula)
- sohcahtoa definitions
- range of values for sine, cosine and tangent for angles of a triangle
- area of a triangle ( 1/2 * side* side * sine of included angle)
- the law of sines
- the pythagorean identity ( sinA ^2 + cosA^2 = 1)
- the cofunction identity ( sin A = cos (90-A))
- the isosceles triangle theorem.
- the pythagorean theorem.
- the law of cosines.
- derivation of a formula for the length of a median in a triangle based on the lengths of the three sides of the triangle.
- angle sum of the angles of a triangle.
- exact values of sine, cosine and tangent for 45, 30 and 60 degrees
- angle of elevation applications
Which formulas apply to all triangles, and which apply ONLY to right triangles?
The student will be able to find the area of any triangle.
The student will be able to find unknown lengths and angle measures in any triangle.
The student will be able to derive the area formula, the law of sines and the law of cosines.
The student will be able to use basic trig identities to rewrite the form of certain trig expressions.
The student will be able to compute the length of the median of a triangle knowing its three sides.
The student will be able to solve angle of elevation applications.
Questions on written tests.
Assignments 1-4, 8, 9, 28
Equations & graphs of lines
- definition of slope (rise/run)
- horizontal / vertical lines
- slope of line = tangent of angle to x-axis
- equations of the coordinate axes
- equation of the y = x line
- equation of the y = - x line
- review of slope-intercept form of the equation of a line.
Does the student really understand what the "equation of a line" represents?
The student will be able to give equations and graph equations of horizontal and vertical lines.
The student will be able to give equation and graph the lines y = x , y = - x.
The student will be able to write an equation for lines from many different combinations of descriptions/ given information.
Questions on written tests.
Assignment 5,6, 7, 8, 9, 10, 11, 31 through 46
Circular Trig.
- socahtoa to represent x = r cos theta, y = r sin theta (parametric representation of unit circle)
- unit circle definitions of sine, cosine and tangent
- "reflection" trig identities ( cos (180-x), sin ( - x), etc.)
-inverse trig command
- using inverse trig and unit circle symmetries to find ALL solutions to simple trig equations ( like sin A = .7 , etc.)
- definition of radian measure and conversion to and from degree measure
- graphs of circular functions, both function and parametric, in both radian and degree mode.
- transformations of the graphs of circular functions
- writing the equation of given graphs of circular functions
Does the student understand the relationship between the "right triangle" sine, cosine and tangent and the "unit circle" sine, cosine and tangent?
The student will be able to state the unit circle definitions of sine, cosine and tangent.
The student will be able to state the exact values of sine, cosine and tangent of quadrantal angles and angles transformationally related to 30, 45, and 60.
The student will be able to use inverse trig and unit circle symmetries to find ALL solutions to simple trig equations ( like sin A = .7 , etc.)
The student will be able to rewrite trignometric expressions using trig identities.
The student will be able to sketch and describe the graph of the six circular functions.
The student will be able to define radian measure, and convert between radians and degrees.
The student will be able to write the equation from the graphs of given circular functions.
The student will be able to solve applications involving circular functions.
Questions on written tests.
"Exact value" quiz for sines, cosines and tangents of angles related to 30, 45 and 60 (NO-CALCULATOR)
Curve sketching quiz on circular functions (NO-CALCULATOR)
- geometric definition of reflection in a line.
- geometric definition of a rotation about a point.
- geometric definition of a translation or a slide.
- geometric definition of a size transformation.
- geometric definition of a glide reflection.
- definition of an isometry.
- properties of and formula for reflection in the x-axis
- properties of and formula for reflection in the y-axis
-properties of and formula for reflection in the y = x line
- properties of and formula for reflection in the y = - x line
- properties of and formula for rotation of 90 degrees about the origin
- properties of and formula for a translation (or slide) - horizontal, vertical or oblique
- properties of and formula for rotation of 180 degrees about the origin
- properties of and formula for rotation of 270 degrees about the origin
- properties of and formula for size transformation centered at (0,0).
- compositions of transformations.
- properties of and formula for scale change centered at (0,0).
-definition of shear on a line
- rotations of any angle theta about the origin
- transformational methods to produce formulas for transformations NOT "centered at (0,0)" (rotations about a point, reflections in any horizontal/ vertical line, size changes centered at a point, etc.)
Does the student understand the connection between the "world of points" and the "world of equations"? Can the student perform transformations to graphs in all of the different representations of equations ( rectangular/ function, polar and parametric)?
The student will be able to state the geometric definition of reflection in a line, a rotation about a point , translation or a slide, a size transformation, a glide reflection and a shear on a line,
The student will be able to state the definition of an isometry.
The student will be able to recognize and use the properties of and formula for: reflection in the x-axis, reflection in the y-axis, reflection in the y = x line, reflection in the y = - x line, shear on x- or y- axis, rotation of 90 degrees about the origin, translation (or slide) - horizontal, vertical or oblique, rotation of 180 degrees about the origin,
rotation of 270 degrees about the origin, size transformation centered at (0,0), scale changes centered at (0,0), shears on the x- or y- axis, rotations of any angle theta about the origin.
The student will be able to create compositions of transformations and formulas for such.
The student will be able to represent displays of transformations on his calculator using lists and scatterplots.
The student will be able to produce formulas for transformations NOT "centered at (0,0)".
Questions on written tests.
Assignment 6, 7
Programming the Ti
- for distance between two points (an introduction)
- to use the law of sines or cosines to compute unknown lengths and angle measures
How does programming help to relieve the tedium of certain mathematical explorations?
The student will be able to create programs on their TIs which perform mathematical functions.
- Pythagorean derivation of formula for distance between two points in a plane.
- area of parallelograms and trapezoids
- using properties of isosceles and equilateral triangles to create algebraic equations and find unknown values.
- finding area and perimeter of regular polygons by triangulation.
- using regular polygons to justify the area formula for a circle.
- area of a triangle- one vertex at (0,0)- using 2x2 matrix determinant formula.
- using regular polygons to justify the formula for the circumference of a circle.
- characteristics and properties of special quadrilaterals
- coordinate proofs of quadrilateral properties
- arc length and arc measure
- relationships between central, inscribed and exterior angles and their intercepted arc measures
- relationships between parts of chord and secant segments which intersect with a circle
- definition of centroid, incenter and orthocenter of a circle
- theorems related to the centroid, incenter and orthocenter of a circle
The student will be able to compute the area and/or perimeter of triangles, parallelograms, trapezoids, regular polygons,circles.
The student will be able to use properties of isosceles and equilateral triangles to create algebraic equations and find unknown values.
The student will understand and apply characteristics and properties of special quadrilaterals
The student will create coordinate proofs of quadrilateral properties
The student will compute arc length and arc measure
The student will understand and apply relationships between central, inscribed and exterior angles and their intercepted arc measures
- The student will understand and apply relationships between parts of chord and secant segments which intersect with a circle
Questions on written tests.
Assignment 15,16,17,18
Geometry of parallel and intersecting lines
- definition of transversal, corresponding, alternate, same-side, interior and exterior angles.
- transformational justification for congruent pairs and supplementary pairs of above.
- definition of vertical angles
- transformational justification for congruent pairs of vertical angles.
The student will be able to identify the classes of angles formed by parallel lines cut by a transversal.
The student will be able to use the congruent or supplementary pairs formed by parallel lines and a transversal, or by vertical angles, to set up algebraic equations and solve for unknown values.
Questions on written tests.
Assignment 14 through 20, 23 through 32, 38
Matrices
- definition, notation and terminology related to matrices and their dimensions
- matrix multiplication, addition and subtraction
- using matrix to list commands and matrix multiplication to perform transformations of figures on the calculator.
- establishing the 2x2 matrix representation for reflections in x-axis, y-axis, y = x, y = -x, rotations of 90,180,270, size and scale changes, shears on the x- and y-axes, and rotations of any angle theta about the origin.
- (application) counting levels of dominance in a closed set using matrix multiplication.
- matrix multiplication to describe compositions of transformations.
- definition of identity and inverse matrices
- inverses of matrices (2x2 by formula, all by augmented matrix/ TI command)
- solving nxn square systems using the matrix inverse method.
- solving matrix equations
- Leontif Input / Output Economic model
Does the student understand the many amazing uses for matrices???
The student will be able to identify the dimensions of a matrix.
The student will be able to demonstrate understanding of the notation used for naming matrices and designating specific elements.
The student will be able to perform basic matrix operations (addition, subtraction, multiplication ) both by hand and on their calculator.
The student will be able to perform all transformations of plotted figures on their calculator using matrix and list commands.
The student will be able to count second level dominances in a round-robin set using matrix multiplication.
The student will be able to use matrix multiplication to describe compositions of transformations.
The student will be able to identify identity and inverse matrices, using formula, augmented matrix method and TI-command.
The student will be able to solve equations with matrix coefficients.
The student will be able to find production levels or demand levels in an economy using the Leontif input/ output matrix model.
Questions on written tests.
QUIZ on augmented matrix method for 3x3 inverse (no calculator).
Assignment 26, 27, 28, 29, 30, 31, 127-129
Advanced trig identities
- rotational derivations for cos (A+-B), sin (A+-B), tan(A+-B).
- substitutional derivations for sin(2P), cos(2P), tan(2P).
- sum-to-product identities
The student will be able to reproduce the derivations of and state the formulas for sin(A+-B), cos(A+-B), tan(A+-B), sin(2P), cos(2P), tan(2P)
The student will be able to advanced trig identities to find exact trig values for certain angles.
The student will be able to rewrite expressions involving trig terms using identities.
Questions on written tests.
Assignment 27, 28, 29, 30, 33 through 48
Parabolas & Quadratic Equations
- geometric definition (focus-directrix) of a parabola.
- equation of "mother" parabola ( y = x^2), its domain and range, both parametric and function/rectangular.
- translations and scale changes of the mother parabola.
- focus/ directrix form of the equation of a parabola
- vertex form of the equation of a parabola
- standard form of the equation of a parabola
- derivation of the quadratic formula (converting general standard form to vertex form, solving for x-intercepts).
- solving quadratic equations using the most appropriate method ( zero-product property, factoring or the quadratic formula)
- newton's projectile motion model (application of quadratic function)
The student will be able to state/ recognize the geometric definition of a parabola.
The student will be able to change correctly from one form of the equation of a parabola to another.
The student will be able to identify important parts of a parabola ( vertex, intercepts, direction, focus, directrix) regardless of the given form of the equation.
The student will be able to write an equation from the graph of a given parabola.
The student will be able to solve applications using quadratic models.
The student will understand the derivation of the quadratic formula.
The student will be able to solve quadratic equations using the most appropriate method ( zero-product property, factoring or the quadratic formula).
The student will be able to answer questions in projectile motion applications using quadratic function analysis and technology.
Questions on written tests.
"Graphing Parabolas" Quiz (no-calc).
Assignment 38 through 48
Systems of Equations
- review of all algebra one methods for solving 2x2 linear systems (substitution, elimination, graphing).
- matrix inverse method for solving square linear systems.
- the geometry of systems (2- and 3- dimension)
- systems involving linear AND quadratic equations.
The student will be able to solve systems using the most appropriate method.
The student will be able to understand the geometric significance of solving nxn square systems.
Table of Contents
Polar coordinates & Complex Numbers
- definition of polar coordinates- converting between polar and rectangular coordinates
- graphs of basic polar equations (circles, roses, spirals)
- rewriting equations between polar and rectangular form
- adding, subtracting, multiplying polar and rectangular points
- polar and rectangular definition of "i"
- complex form of polar / rectangular points
- operations on complex numbers
- understand and apply the definition of polar coordinates
- convert between polar and rectangular coordinates
- graph the basic polar equations (circles, roses, spirals)
- rewrite equations between polar and rectangular form
- add, subtract, multiply polar and rectangular points
- understand and apply polar and rectangular definition of "i"
- understand and apply the complex form of polar / rectangular points
- perform operations on complex numbers
Sequences & Series
- definition of arithmetic sequence- definition of geometric sequence
- recursive and explicit formulas for the Nth term of an arithmetic or geometric sequence
- explicit formulas for the Nth sum of an arithmetic or geometric sequence
- formula for the sum of an infinite geometric sequence
- derivation of amortized interest formula
- derivation of euler's formula ( e^i*pi+1=0)
- understand and apply the definition of arithmetic sequence
- understand and apply the definition of geometric sequence
- write and apply both recursive and explicit formulas for the Nth term of an arithmetic or geometric sequence
- write and apply explicit formulas for the Nth sum of an arithmetic or geometric sequence
- write and apply formula for the sum of an infinite geometric sequence
- understand the derivation of amortized interest formula, and apply the formula to loan situations
- understand the derivation of euler's formula
( e^i*pi+1=0)
Subsets and operations of real numbers
- definition of rational and irrational- irrationality of square roots
- which operations "distribute" correctly over others?
- nth roots, radicals and rational exponents
- density of integers, rationals, irrationals, etc.
- "rationalizing denominators"
- abstract definitions of identity element and inverse for a set under a given operation.
- definition of/ properties of base-N numeral
- conversion among base-N numbers.
The student will be able to convert any decimal number into its equivalent rational form.
The student will be able to identify or complete correct examples of distribution.
The student will be able to understand the mathematical/technological representations of a "number".
The student will be able to rewrite radical expressions with rational denominators.
The student will be able to identify the identity element of a set, and identify the inverse of each element.
The student will be able to convert among base-N numbers.
Triangle trig
- area of a triangle (1/2 bh formula)- sohcahtoa definitions
- range of values for sine, cosine and tangent for angles of a triangle
- area of a triangle ( 1/2 * side* side * sine of included angle)
- the law of sines
- the pythagorean identity ( sinA ^2 + cosA^2 = 1)
- the cofunction identity ( sin A = cos (90-A))
- the isosceles triangle theorem.
- the pythagorean theorem.
- the law of cosines.
- derivation of a formula for the length of a median in a triangle based on the lengths of the three sides of the triangle.
- angle sum of the angles of a triangle.
- exact values of sine, cosine and tangent for 45, 30 and 60 degrees
- angle of elevation applications
The student will be able to find unknown lengths and angle measures in any triangle.
The student will be able to derive the area formula, the law of sines and the law of cosines.
The student will be able to use basic trig identities to rewrite the form of certain trig expressions.
The student will be able to compute the length of the median of a triangle knowing its three sides.
The student will be able to solve angle of elevation applications.
Equations & graphs of lines
- definition of slope (rise/run)- horizontal / vertical lines
- slope of line = tangent of angle to x-axis
- equations of the coordinate axes
- equation of the y = x line
- equation of the y = - x line
- review of slope-intercept form of the equation of a line.
The student will be able to give equation and graph the lines y = x , y = - x.
The student will be able to write an equation for lines from many different combinations of descriptions/ given information.
Circular Trig.
- socahtoa to represent x = r cos theta, y = r sin theta (parametric representation of unit circle)- unit circle definitions of sine, cosine and tangent
- "reflection" trig identities ( cos (180-x), sin ( - x), etc.)
-inverse trig command
- using inverse trig and unit circle symmetries to find ALL solutions to simple trig equations ( like sin A = .7 , etc.)
- definition of radian measure and conversion to and from degree measure
- graphs of circular functions, both function and parametric, in both radian and degree mode.
- transformations of the graphs of circular functions
- writing the equation of given graphs of circular functions
The student will be able to state the exact values of sine, cosine and tangent of quadrantal angles and angles transformationally related to 30, 45, and 60.
The student will be able to use inverse trig and unit circle symmetries to find ALL solutions to simple trig equations ( like sin A = .7 , etc.)
The student will be able to rewrite trignometric expressions using trig identities.
The student will be able to sketch and describe the graph of the six circular functions.
The student will be able to define radian measure, and convert between radians and degrees.
The student will be able to write the equation from the graphs of given circular functions.
The student will be able to solve applications involving circular functions.
"Exact value" quiz for sines, cosines and tangents of angles related to 30, 45 and 60 (NO-CALCULATOR)
Curve sketching quiz on circular functions (NO-CALCULATOR)
Transformations
- geometric definition of reflection in a line.- geometric definition of a rotation about a point.
- geometric definition of a translation or a slide.
- geometric definition of a size transformation.
- geometric definition of a glide reflection.
- definition of an isometry.
- properties of and formula for reflection in the x-axis
- properties of and formula for reflection in the y-axis
-properties of and formula for reflection in the y = x line
- properties of and formula for reflection in the y = - x line
- properties of and formula for rotation of 90 degrees about the origin
- properties of and formula for a translation (or slide) - horizontal, vertical or oblique
- properties of and formula for rotation of 180 degrees about the origin
- properties of and formula for rotation of 270 degrees about the origin
- properties of and formula for size transformation centered at (0,0).
- compositions of transformations.
- properties of and formula for scale change centered at (0,0).
-definition of shear on a line
- rotations of any angle theta about the origin
- transformational methods to produce formulas for transformations NOT "centered at (0,0)" (rotations about a point, reflections in any horizontal/ vertical line, size changes centered at a point, etc.)
The student will be able to state the definition of an isometry.
The student will be able to recognize and use the properties of and formula for: reflection in the x-axis, reflection in the y-axis, reflection in the y = x line, reflection in the y = - x line, shear on x- or y- axis, rotation of 90 degrees about the origin, translation (or slide) - horizontal, vertical or oblique, rotation of 180 degrees about the origin,
rotation of 270 degrees about the origin, size transformation centered at (0,0), scale changes centered at (0,0), shears on the x- or y- axis, rotations of any angle theta about the origin.
The student will be able to create compositions of transformations and formulas for such.
The student will be able to represent displays of transformations on his calculator using lists and scatterplots.
The student will be able to produce formulas for transformations NOT "centered at (0,0)".
Programming the Ti
- for distance between two points (an introduction)- to use the law of sines or cosines to compute unknown lengths and angle measures
Geometry: Polygons and other plane figures
- Pythagorean derivation of formula for distance between two points in a plane.- area of parallelograms and trapezoids
- using properties of isosceles and equilateral triangles to create algebraic equations and find unknown values.
- finding area and perimeter of regular polygons by triangulation.
- using regular polygons to justify the area formula for a circle.
- area of a triangle- one vertex at (0,0)- using 2x2 matrix determinant formula.
- using regular polygons to justify the formula for the circumference of a circle.
- characteristics and properties of special quadrilaterals
- coordinate proofs of quadrilateral properties
- arc length and arc measure
- relationships between central, inscribed and exterior angles and their intercepted arc measures
- relationships between parts of chord and secant segments which intersect with a circle
- definition of centroid, incenter and orthocenter of a circle
- theorems related to the centroid, incenter and orthocenter of a circle
The student will be able to use properties of isosceles and equilateral triangles to create algebraic equations and find unknown values.
The student will understand and apply characteristics and properties of special quadrilaterals
The student will create coordinate proofs of quadrilateral properties
The student will compute arc length and arc measure
The student will understand and apply relationships between central, inscribed and exterior angles and their intercepted arc measures
- The student will understand and apply relationships between parts of chord and secant segments which intersect with a circle
Geometry of parallel and intersecting lines
- definition of transversal, corresponding, alternate, same-side, interior and exterior angles.- transformational justification for congruent pairs and supplementary pairs of above.
- definition of vertical angles
- transformational justification for congruent pairs of vertical angles.
The student will be able to use the congruent or supplementary pairs formed by parallel lines and a transversal, or by vertical angles, to set up algebraic equations and solve for unknown values.
Matrices
- definition, notation and terminology related to matrices and their dimensions- matrix multiplication, addition and subtraction
- using matrix to list commands and matrix multiplication to perform transformations of figures on the calculator.
- establishing the 2x2 matrix representation for reflections in x-axis, y-axis, y = x, y = -x, rotations of 90,180,270, size and scale changes, shears on the x- and y-axes, and rotations of any angle theta about the origin.
- (application) counting levels of dominance in a closed set using matrix multiplication.
- matrix multiplication to describe compositions of transformations.
- definition of identity and inverse matrices
- inverses of matrices (2x2 by formula, all by augmented matrix/ TI command)
- solving nxn square systems using the matrix inverse method.
- solving matrix equations
- Leontif Input / Output Economic model
The student will be able to demonstrate understanding of the notation used for naming matrices and designating specific elements.
The student will be able to perform basic matrix operations (addition, subtraction, multiplication ) both by hand and on their calculator.
The student will be able to perform all transformations of plotted figures on their calculator using matrix and list commands.
The student will be able to count second level dominances in a round-robin set using matrix multiplication.
The student will be able to use matrix multiplication to describe compositions of transformations.
The student will be able to identify identity and inverse matrices, using formula, augmented matrix method and TI-command.
The student will be able to solve equations with matrix coefficients.
The student will be able to find production levels or demand levels in an economy using the Leontif input/ output matrix model.
QUIZ on augmented matrix method for 3x3 inverse (no calculator).
Advanced trig identities
- rotational derivations for cos (A+-B), sin (A+-B), tan(A+-B).- substitutional derivations for sin(2P), cos(2P), tan(2P).
- sum-to-product identities
The student will be able to advanced trig identities to find exact trig values for certain angles.
The student will be able to rewrite expressions involving trig terms using identities.
Parabolas & Quadratic Equations
- geometric definition (focus-directrix) of a parabola.
- equation of "mother" parabola ( y = x^2), its domain and range, both parametric and function/rectangular.
- translations and scale changes of the mother parabola.
- focus/ directrix form of the equation of a parabola
- vertex form of the equation of a parabola
- standard form of the equation of a parabola
- derivation of the quadratic formula (converting general standard form to vertex form, solving for x-intercepts).
- solving quadratic equations using the most appropriate method ( zero-product property, factoring or the quadratic formula)
- newton's projectile motion model (application of quadratic function)
The student will be able to change correctly from one form of the equation of a parabola to another.
The student will be able to identify important parts of a parabola ( vertex, intercepts, direction, focus, directrix) regardless of the given form of the equation.
The student will be able to write an equation from the graph of a given parabola.
The student will be able to solve applications using quadratic models.
The student will understand the derivation of the quadratic formula.
The student will be able to solve quadratic equations using the most appropriate method ( zero-product property, factoring or the quadratic formula).
The student will be able to answer questions in projectile motion applications using quadratic function analysis and technology.
"Graphing Parabolas" Quiz (no-calc).
Systems of Equations
- review of all algebra one methods for solving 2x2 linear systems (substitution, elimination, graphing).
- matrix inverse method for solving square linear systems.
- the geometry of systems (2- and 3- dimension)
- systems involving linear AND quadratic equations.
The student will be able to understand the geometric significance of solving nxn square systems.